My research is in quantum information theory and its connections to mathematics, fundamental physics & computing. I am in part supported by an NWO Veni grant on Quantum bits in space and time. I am part of the NWA quantum/nano route and a member of the Geometry and Quantum Theory mathematical research cluster.
Motivated by quantum information, I also study mathematical problems in representation theory and invariant theory through the lens of classical and quantum computation.
Curriculum vitae: [pdf]
Together with Peter Bürgisser, I am organizing a minisymposium on “Efficient algorithms for geometric invariant theory” at the SIAM Conference on Applied Algebraic Geometry 2019.
I am currently looking to hire a postdoc in quantum information science. For more information and to apply, see here. The position is now filled.
Together with Ankit Garg, Rafael Oliveira, and Avi Wigderson, I organized a workshop on scaling algorithms and applications at FOCS 2018. See here for details.
- Bas Dirkse (PhD candidate), multiparty protocols for quantum networks
- Yinan Li (postdoctoral researcher)
- Freek Witteveen (PhD candidate), quantum information & field theory
- Emma Loos (MSc project)
- Jeroen Dekker (MSc project)
- Philip Verduyn Lunel (MSc project)
- Lars van Geest (BSc project, co-supervised by Maris Ozols)
- Raja Damanik (MSc project on optimality in stabilizer testing)
- Casper Guyrik (MSc project on quantum algorithms for factoring and post-quantum RSA, supervised by Ronald de Wolf)
- Philip Roeleveld (BSc project on a truncated tensor scaling algorithm)
- Wouter Borg (BSc project on entanglement in the stabilizer formalism)
Next group meeting: See Slack.
Publications and Preprints
In Spring 2019, Maris Ozols and I offer a course on Quantum Information Theory in the MasterMath program. See here for more information.
Guus Regts and I also organize the Master Seminar in Algebra, Geometry and Mathematical Physics, see here. This term, we are following Sagan’s book “The Symmetric Group”. Here is a refresher on basic representation theory roughly following Sections 1.1–1.6.
See here for introductory lectures on quantum information, field theory, and gravity (with an emphasis on links between these fields).
In Spring 2018, I tought a course on Symmetry and Quantum Information at UvA. See here for all course material. I previously taught a similar course at Stanford University. Watch this lecture as a teaser. I also taught an abridged version of this course at IES in Cargese.
Quantum Software and Society
- Nature Insight
- Quantum software manifesto
- Ronald de Wolf’s essay on the impact of quantum computing on society
- John Preskill’s essay on noisy intermediate-scale quantum technology
- Gate-level quantum software platforms overview as of July 2018
- “Quantum Marginals, Entanglement, and Symmetries”, DPG 2019 [pdf]
- “Quantum circuits for the Dirac field in 1+1 dimensions”, AEI 2019 [pdf] [video]
- “An invitation to tensor networks”, IAS 2018 [video]
- “Quantum Information and Holography”, DESY 2018 [pdf] [video]
- “Schur-Weyl Duality for the Clifford Group: Property testing, de Finetti representations, and a robust Hudson theorem”, QIP 2018, Boulder 2018, Bad Honnef 2018 [pdf] [video] [pdf] [pdf]
- “Quantum entanglement and space-time”, Groningen 2018 [html] [video]
- “Convexity, marginals, and moment polytopes”, IAS 2018 [pdf] [video]
- “Introduction to Quantum Programming”, QuSoft 2018
- “Quantum marginal problem, tensor scaling, and invariant theory”, NMC 2018 [pdf]
- “Rigorous entanglement renormalization from wavelets”, KITP 2017, Caltech 2017, AEI 2018, Amsterdam 2018, GGI 2018 [pdf] [video] [pdf] [pdf] [pdf]
- “When is a quantum state a stabilizer state?”, QuSoft 2017, QuTech 2018 [pdf]
- “Bulk reconstruction, error correction, and recovery maps”, KITP 2017 [video]
- “Tensor network models of holography”, DESY 2017
- “When is a state a stabilizer state? Testing stabilizer states with six copies”, CWI 2017
- “Tensors and Quantum Physics”, Auburn 2017 [video]
- “Multiparty entanglement, random codes, and quantum gravity”, Coogee 2017 [pdf], “Multipartite entanglement in toy models of holography”, Simons Center for Geometry & Physics 2016 [pdf] [video]
- “Entanglement in random tensor networks”, Georgia Tech 2016 [pdf]
- “Holographic duality from random tensor networks”, MIT 2015, KITP 2016, Cologne 2016, IQC 2016 [pdf] [pdf] [video] [other]
- “Moment polytopes & computational complexity”, Berkeley 2015 [pdf]
- “The Holographic Entropy Cone”, ETHZ, Caltech, CRM 2015; QIP 2016 [pdf short] [video] [pdf long]
- “Kronecker coefficients and complexity theory”, Dartmouth 2015, Rome 2016 [pdf]
- “Topologically ordered models in higher dimensions”, QGQIT 2015 [pdf]
- “Random Quantum Marginals”, IAS 2014 [video]
- “A Heisenberg Limit for Quantum Region Estimation”, ISIT 2014 [pdf]
- “The Quantum Marginal Problem”, DPG Spring Meeting 2014 [pdf]
- “Entanglement Polytopes”, QIP 2013; QSIT Lunch Seminar [pdf] [video] [science] [pdf] [explorer]
- “Quantum Entropies and Representation Theory”, IHES 2013 [pdf]
- “Computing Multiplicities of Lie Group Representations”, FOCS 2012 [pdf] [video]
- “Quantum State Tomography of 1000 Bosons”, SPS Meeting 2012 [pdf]
- “Quantum Marginals and Classical Moments”, IMS 2013 [pdf]
- “Eigenvalue Distributions of Reduced Density Matrices”, ICMP 2012 [pdf]
- Solve the quantum marginal problem and compute entanglement polytopes using our new tensor scaling algorithm.
- Use wavelets to approximate ground states of free fermion theories.
- Prove new holographic entropy inequalities using the contractor
- Just a moment! – an algorithm for computing moment cones for the quantum marginal problem
- Explore entanglement polytopes
- Compute Kronecker coefficients using barvikron (Python) or the new Kronecker Maple package
- Download the quantum sandbox for Octave/Matlab